Internal problem ID [2750]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 18.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+y^{\prime }-x \cos \relax (x )-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 31
dsolve(diff(y(x),x$3)+diff(y(x),x)=sin(x)+x*cos(x),y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) c_{1}-\cos \relax (x ) c_{2}-\frac {\cos \relax (x ) x^{2}}{4}+\frac {\cos \relax (x )}{2}+\frac {x \sin \relax (x )}{4}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 36
DSolve[y'''[x]+y'[x]==Sin[x]+x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{8} \left (2 x^2-3+8 c_2\right ) \cos (x)+\left (\frac {x}{4}+c_1\right ) \sin (x)+c_3 \\ \end{align*}